fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ecanonical_2ESPconst_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPconst_2E1(s(A_27a,X0_2E0))) = s(tyop_2Ecanonical_2Espolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ecanonical_2Espolynom(A_27a)),c_2Ecanonical_2ESPconst_2E0),s(A_27a,X0_2E0))))).
fof(arityeq1_2Ec_2Ecanonical_2ESPvar_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPvar_2E1(s(tyop_2Equote_2Eindex,X0_2E0))) = s(tyop_2Ecanonical_2Espolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Ecanonical_2Espolynom(A_27a)),c_2Ecanonical_2ESPvar_2E0),s(tyop_2Equote_2Eindex,X0_2E0))))).
fof(arityeq2_2Ec_2Ecanonical_2ESPmult_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPmult_2E2(s(tyop_2Ecanonical_2Espolynom(A_27a),X0_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),X1_2E0))) = s(tyop_2Ecanonical_2Espolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Espolynom(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Espolynom(A_27a))),c_2Ecanonical_2ESPmult_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),X0_2E0))),s(tyop_2Ecanonical_2Espolynom(A_27a),X1_2E0))))).
fof(arityeq2_2Ec_2Ecanonical_2ESPplus_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPplus_2E2(s(tyop_2Ecanonical_2Espolynom(A_27a),X0_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),X1_2E0))) = s(tyop_2Ecanonical_2Espolynom(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Espolynom(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Ecanonical_2Espolynom(A_27a))),c_2Ecanonical_2ESPplus_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),X0_2E0))),s(tyop_2Ecanonical_2Espolynom(A_27a),X1_2E0))))).
fof(arityeq5_2Ec_2Ecanonical_2Espolynom__CASE_2E5_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0]: (s(A_27b,c_2Ecanonical_2Espolynom__CASE_2E5(s(tyop_2Ecanonical_2Espolynom(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),X3_2E0),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),X4_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),A_27b))))),c_2Ecanonical_2Espolynom__CASE_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),X4_2E0))))).
fof(canonicalTheory_2Espolynom__case__cong,axiom,![A_27a, A_27b]: ![V0f3_27_2E0, V1f2_27_2E0, V2f1_27_2E0, V3f_27_2E0, V4M_2E0, V5M_27_2E0, V6f_2E0, V7f1_2E0, V8f2_2E0, V9f3_2E0]: (((s(tyop_2Ecanonical_2Espolynom(A_27a),V4M_2E0) = s(tyop_2Ecanonical_2Espolynom(A_27a),V5M_27_2E0)) & (![V10a_2E0]: ((s(tyop_2Ecanonical_2Espolynom(A_27a),V5M_27_2E0) = s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPvar_2E1(s(tyop_2Equote_2Eindex,V10a_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),V6f_2E0),s(tyop_2Equote_2Eindex,V10a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),V3f_27_2E0),s(tyop_2Equote_2Eindex,V10a_2E0))))) & (![V11a_2E0]: ((s(tyop_2Ecanonical_2Espolynom(A_27a),V5M_27_2E0) = s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPconst_2E1(s(A_27a,V11a_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7f1_2E0),s(A_27a,V11a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_27_2E0),s(A_27a,V11a_2E0))))) & (![V12a0_2E0, V13a1_2E0]: ((s(tyop_2Ecanonical_2Espolynom(A_27a),V5M_27_2E0) = s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPplus_2E2(s(tyop_2Ecanonical_2Espolynom(A_27a),V12a0_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),V13a1_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V8f2_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),V12a0_2E0))),s(tyop_2Ecanonical_2Espolynom(A_27a),V13a1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V1f2_27_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),V12a0_2E0))),s(tyop_2Ecanonical_2Espolynom(A_27a),V13a1_2E0))))) & ![V14a0_2E0, V15a1_2E0]: ((s(tyop_2Ecanonical_2Espolynom(A_27a),V5M_27_2E0) = s(tyop_2Ecanonical_2Espolynom(A_27a),c_2Ecanonical_2ESPmult_2E2(s(tyop_2Ecanonical_2Espolynom(A_27a),V14a0_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),V15a1_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V9f3_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),V14a0_2E0))),s(tyop_2Ecanonical_2Espolynom(A_27a),V15a1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V0f3_27_2E0),s(tyop_2Ecanonical_2Espolynom(A_27a),V14a0_2E0))),s(tyop_2Ecanonical_2Espolynom(A_27a),V15a1_2E0))))))))) => (s(A_27b,c_2Ecanonical_2Espolynom__CASE_2E5(s(tyop_2Ecanonical_2Espolynom(A_27a),V4M_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V8f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V9f3_2E0))) = s(A_27b,c_2Ecanonical_2Espolynom__CASE_2E5(s(tyop_2Ecanonical_2Espolynom(A_27a),V5M_27_2E0),s(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27b),V3f_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V1f2_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),tyop_2Emin_2Efun(tyop_2Ecanonical_2Espolynom(A_27a),A_27b)),V0f3_27_2E0)))))).
